Acoustic techniques are commonly used for imaging the subsurface in the context of hydrocarbon exploration and production. In a common approach, seismic signals are transmitted into the subsurface by sources at the earth's surface or in a borehole. Seismic receivers detect and record the resulting acoustic signals. The received signals, and particularly those that have been reflected and/or refracted in the subsurface, will contain information about the subsurface. Thus, for example, wave equation migration methods such as Reverse Time Migration (RTM) have been critical to imaging beneath complex overburdens such as salt. Despite theoretical and algorithmic improvements, proper post-processing of the migrated image is often a key step in producing optimum imaging quality.
An example of such post-processing is muting of far offset arrivals on image domain gathers where a proper muting can make or break the quality of the final image. In the case of Kirchhoff migration, this is easily and naturally done on post-migration midpoint-offset gathers. Muting is equally important for Wave Equation migration; however, generating appropriate image gathers for this process is a more costly proposition than simply migration output to stack.
Muting or angle weighting of post-RTM data is most correctly performed in the subsurface angle gather domain. Various authors describe methods for computing angle gathers for wave equation migration (de Bruin et al., 1990; Prucha et al., 1999; Mosher and Foster, 2000; Rickett and Sava, 2002; Xie and Wu, 2002; Sava and Fomel, 2003; Soubaras, 2003), but the main impediment is the cost of computing and storing large amounts of output data for full azimuth subsurface angle gathers.
Shot to Image Gathers (SIGs) are a much cheaper alternative to wave equation angle gathers. They are formed by collecting the output from all the individually migrated shots from shot record wave equation migration e.g., Reverse Time Migration. Normally the output images from each shot are stacked together. As illustrated in FIG. 1, Each SIG is formed by collecting the traces at a common output image location and then assigning a vector distance (vector offset) based on the horizontal distance from the image point to the shot location. The result is an SIG such as is shown in FIG. 2. These gathers provide a space where muting can be applied according to this distance.
One complication is that SIG gathers have a dip component that shifts the center of energy away from the zero ‘offset,’ which makes muting more difficult than with conventional image gathers. A data-dependent mute function would address this issue, but a useful data-dependent mute function can be difficult to compute in areas with poor signal to noise or where the illumination is variable.
Hence, it remains desirable to provide a simple and inexpensive method for deriving and applying optimal weighting coefficients for RTM shot-image gathers so as to improve the overall S/N ratio of the final stack.